Question

What is the constant difference for the following sequence? 8 28 90 202 372 608 * 2 points 1st 2nd 3rd 4th

Answer 1

To find the constant difference in the given sequence \(8, 28, 90, 202, 372, 608\), we will first calculate the first differences between consecutive terms, and then the second differences, and so on until we detect a constant difference.

1. **First differences:**
- \( 28 - 8 = 20 \)
- \( 90 - 28 = 62 \)
- \( 202 - 90 = 112 \)
- \( 372 - 202 = 170 \)
- \( 608 - 372 = 236 \)

So the first differences are: \( 20, 62, 112, 170, 236 \).

2. **Second differences:**
- \( 62 - 20 = 42 \)
- \( 112 - 62 = 50 \)
- \( 170 - 112 = 58 \)
- \( 236 - 170 = 66 \)

So the second differences are: \( 42, 50, 58, 66 \).

3. **Third differences:**
- \( 50 - 42 = 8 \)
- \( 58 - 50 = 8 \)
- \( 66 - 58 = 8 \)

The third differences are constant: \( 8, 8, 8 \).

Since the third differences are constant, this means that the sequence is polynomial of degree 3 (cubic).

Thus, the answer to your question regarding the "constant difference" is found at the **third** level. The constant difference is \(8\).

Therefore, the correct response based on your options is **4th** (indicating the constant difference occurs at the 4th level of differences).